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Related Concept Videos

IR Spectroscopy: Hooke's Law Approximation of Molecular Vibration01:16

IR Spectroscopy: Hooke's Law Approximation of Molecular Vibration

A covalently bonded heteronuclear diatomic molecule can be modeled as two vibrating masses connected by a spring. The vibrational frequency of the bond can be expressed using an equation derived from Hooke's law, which describes how the force applied to stretch or compress a spring is proportional to the displacement of the spring. In this case, the atoms behave like masses, and the bond acts like a spring.
According to Hooke's law, the vibrational frequency is directly proportional to the...
IR Spectrum Peak Splitting: Symmetric vs Asymmetric Vibrations01:08

IR Spectrum Peak Splitting: Symmetric vs Asymmetric Vibrations

Identical bonds within a polyatomic group can stretch symmetrically (in-phase) or asymmetrically (out-of-phase). Similar to hydrogen bonding, these vibrations also influence the shape of the IR peak. Generally, asymmetric stretching frequencies are higher than symmetric stretching frequencies. For example, primary amines exhibit two distinct IR peaks between 3300–3500 cm−1 corresponding to the symmetric and asymmetric N-H stretching, while secondary amines exhibit a single stretching vibration...
¹H NMR: Interpreting Distorted and Overlapping Signals01:02

¹H NMR: Interpreting Distorted and Overlapping Signals

Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are slanted or...
2D NMR: Heteronuclear Single-Quantum Correlation Spectroscopy (HSQC)01:19

2D NMR: Heteronuclear Single-Quantum Correlation Spectroscopy (HSQC)

Heteronuclear single-quantum correlation spectroscopy (HSQC) is a 2D NMR technique that reveals one-bond correlations between hydrogen and a heteronucleus. The HSQC experiment is similar to the heteronuclear correlation experiment (HETCOR) but is more sensitive. In the HSQC spectrum, the proton chemical shift is plotted on the horizontal F2 axis, while the 13C chemical shift is plotted on the vertical F1 axis. The corresponding proton and 13C spectra are also shown. The HSQC contour plot does...
Characteristics of Simple Harmonic Motion01:17

Characteristics of Simple Harmonic Motion

The key characteristic of the simple harmonic motion is that the acceleration of the system and, therefore, the net force are proportional to the displacement and act in the opposite direction to the displacement. Additionally, the period and frequency of a simple harmonic oscillator are independent of its amplitude. For example, diving boards move faster or slower based on their thickness. A stiff, thick diving board has a large force constant, which causes it to have a smaller period, while a...
Generalized Hooke's Law01:22

Generalized Hooke's Law

The generalized Hooke's Law is a broadened version of Hooke's Law, which extends to all types of stress and in every direction. Consider an isotropic material shaped into a cube subjected to multiaxial loading. In this scenario, normal stresses are exerted along the three coordinate axes. As a result of these stresses, the cubic shape deforms into a rectangular parallelepiped. Despite this deformation, the new shape maintains equal sides, and there is a normal strain in the direction of the...

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Rapid anharmonic vibrational corrections derived from partial Hessian analysis.

Magnus W D Hanson-Heine1, Michael W George, Nicholas A Besley

  • 1School of Chemistry, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom.

The Journal of Chemical Physics
|June 21, 2012
PubMed
Summary
This summary is machine-generated.

This study introduces a new computational method for calculating anharmonic vibrational frequencies. The partial Hessian approach efficiently determines localized vibrational modes, reducing computational cost while maintaining accuracy.

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Area of Science:

  • Computational Chemistry
  • Molecular Spectroscopy
  • Theoretical Chemistry

Background:

  • Vibrational analysis is crucial for understanding molecular properties.
  • Accurate calculation of anharmonic frequencies is computationally intensive.
  • Localized vibrational modes require efficient analytical methods.

Purpose of the Study:

  • To develop a computationally efficient method for calculating anharmonic vibrational frequencies.
  • To enable accurate analysis of localized vibrational modes.
  • To reduce the computational cost of anharmonic frequency calculations.

Main Methods:

  • Partial Hessian framework for vibrational analysis.
  • Second-order vibrational perturbation theory.
  • Transition optimized shifted Hermite method.
  • Calculation of anharmonic frequencies for localized modes.

Main Results:

  • The partial Hessian approach successfully describes vibrational properties of localized modes.
  • Anharmonic frequencies for spatially localized vibrational modes were determined at reduced computational cost.
  • The method demonstrated effectiveness across diverse systems: organic molecules on surfaces, model peptides, and polycyclic aromatic hydrocarbons.
  • Calculated anharmonic frequencies closely matched full anharmonic calculations.

Conclusions:

  • The partial Hessian approach offers a significant reduction in computational cost for anharmonic frequency calculations.
  • This method provides an accurate and efficient way to study localized vibrational modes.
  • The developed approach is broadly applicable to various molecular systems.